McMullen showed in [1]} that the Julia set of any exponential function \(z\mapsto \lambda e^z\) , \(\lambda \ne 0\) , has Hausdorff dimension equal to 2
and that the Julia set of any sine function \(z\mapsto \sin (\alpha z +\beta )\) , \(\alpha \ne 0\) , has even positive Lebesgue measure. His result has been extended by Barański
[2]} and Schubert [3]} to all entire functions in
class \(\mathcal {B}\)  that have finite order.
As it is mentioned in [4]}, their proof actually shows that
\(\text{{\rm HD}}(\mathcal {I}(f)) =2\) 
